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Search: 8, 12, 18, 27, 40, 58
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| A063978 |
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Sum_{i for which n - i*(i-1)/2 >= 0} binomial (n - i*(i-1)/2, i). |
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+20
2
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| 1, 2, 3, 5, 8, 12, 18, 27, 40, 58, 83, 118, 167, 235, 328, 454, 624, 853, 1161, 1574, 2125, 2856, 3821, 5090, 6754, 8931, 11773, 15474, 20280, 26502, 34533, 44870, 58142, 75145, 96885, 124630, 159973, 204909, 261930, 334143, 425417, 540566
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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E. Deutsch, E. Munarini and S. Rinaldi, Skew Dyck Paths. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 29 2009]
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FORMULA
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G.f.: Sum(x^(k*(k-1)/2)/(1-x)^k, k=1..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 25 2004
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MATHEMATICA
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Table[ Sum[ Binomial[ n - i(i - 1)/2, i], {i, 0, Floor[ (Sqrt[8n + 1] - 1)/2]} ], {n, 0, 40}]
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CROSSREFS
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Cf. A064188.
Sequence in context: A007478 A014605 A132842 this_sequence A077868 A109537 A081226
Adjacent sequences: A063975 A063976 A063977 this_sequence A063979 A063980 A063981
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KEYWORD
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nonn
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AUTHOR
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Helmut Schnitzspan (HSchnitzspan(AT)gmx.de), Sep 05 2001
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EXTENSIONS
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More terms from Dean Hickerson, Sep 06 2001
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| A064188 |
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Sum_{ i = 0 .. floor(n/2)} binomial (n - i*(i-1)/2, i). |
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+20
2
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| 1, 3, 4, 8, 12, 18, 27, 40, 58, 83, 118, 195, 242, -1387, -338, 75876, 44491, -3099115, -2028539, 129829195, 91749709, -5687984421, -4236497556, 263653557716, 204087552038, -12979768392096, -10348229609729, 679042377362009, 554161706136054, -37712174126966326
(list; graph; listen)
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OFFSET
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0,2
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MATHEMATICA
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Table[ Sum[ Binomial[ n - i*(i - 1)/2, i ], {i, 0, Floor[ n/2 ] } ], {n, 1, 30} ]
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CROSSREFS
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Cf. A063978.
Sequence in context: A077434 A076136 A146566 this_sequence A147620 A088953 A025034
Adjacent sequences: A064185 A064186 A064187 this_sequence A064189 A064190 A064191
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KEYWORD
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sign
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AUTHOR
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Helmut Schnitzspan (HSchnitzspan(AT)gmx.de), Sep 05 2001
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 06 2001
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| 1, 1, 2, 3, 5, 8, 12, 18, 27, 40, 58, 83, 118, 167, 234, 326, 451, 621, 850, 1157, 1567, 2113, 2837, 3794, 5054, 6708, 8873, 11697, 15371, 20137, 26305, 34267, 44520, 57692, 74576, 96172, 123736, 158846, 203480, 260115, 331845, 422532, 536985
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A132841 forms the least increasing logarithmic coefficients such that exponentiation results in an integer sequence.
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EXAMPLE
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A(x) = 1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + 12x^6 + 18x^7 + 27x^8 +...
log(A(x)) = x + 3x^2/2 + 4x^3/3 + 7x^4/4 + 11x^5/5 + 12x^6/6 +...(A132841).
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CROSSREFS
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Cf. A132841.
Sequence in context: A078408 A007478 A014605 this_sequence A063978 A077868 A109537
Adjacent sequences: A132839 A132840 A132841 this_sequence A132843 A132844 A132845
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Sep 12 2007
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